Simplify; express your answer in exponential form. Assume $q\neq 0, a\neq 0$. $\dfrac{{(qa^{-5})^{2}}}{{q^{-1}a^{-4}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(qa^{-5})^{2} = (q)^{2}(a^{-5})^{2}}$ On the left, we have ${q}$ to the exponent ${2}$ . Now ${1 \times 2 = 2}$ , so ${(q)^{2} = q^{2}}$ Apply the ideas above to simplify the equation. $\dfrac{{(qa^{-5})^{2}}}{{q^{-1}a^{-4}}} = \dfrac{{q^{2}a^{-10}}}{{q^{-1}a^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{2}a^{-10}}}{{q^{-1}a^{-4}}} = \dfrac{{q^{2}}}{{q^{-1}}} \cdot \dfrac{{a^{-10}}}{{a^{-4}}} = q^{{2} - {(-1)}} \cdot a^{{-10} - {(-4)}} = q^{3}a^{-6}$